Quantum Degenerates

Thursday, 14 May 2009

Again I am busy. Sometime I intend to do a post about the truncated Wigner method of simulating quantum and thermal fluctuations. In the meantime here is an interesting blog post about atom interferometry and Steve Chu.

Monday, 4 May 2009

In my research I am largely concerned with 1D gasses of bosons (particles with integer spin). One of the reasons I model 1D is that it is quicker and easier than running 3D simulations/ doing 3D calculations. However, 1D systems display many effects that 3D systems do not. For the purposes of this article, I will assume that the atoms interact with each other via a repulsive force.

At a critical temperature (very close to absolute zero), ideal 3D bose gasses will condense into a Bose-Einstein condensate, where many atoms occupy the same quantum state. Fluctuations in the density of the gas are suppressed and there is phase coherence across the system (the condensate may be described by a complex-valued wavefunction). Such a system is exhibits the famous quantum-mechanical particle-wave duality, but on a (nearly) macroscopic scale.

This paper (arxiv) shows the phase diagram (below) of a 1D bose gas is somewhat more complicated.

In an infinite-sized 1D system, a Bose gas cannot condense into such a Bose-Einstein condensate, since phase fluctations destroy the coherence across the system. In this case, the density fluctations are still supressed, and the system is called a quasi-condensate. In a finite system, at sufficiently low temperature and high atom number, the phase fluctuations may be of such large wavelength that they are bigger than the size of the system itself, and the gas behaves exactly as a true Bose-Einstein condensate.

This is not the entire picture; if a gas is sufficiently dilute, or the repulsive interactions are strong, the atoms can be thought of as localised individual particles. In 1D, the particles cannot pass each other, as in higher dimensional systems. As a consequence of this, the atoms gain some properties of Fermi atoms (such Fermionised bosons cannot occupy the same position state - however, unlike Fermions, they can still occupy the same momentum state). This system is called a Tonks gas.

Moreover, when the inter-particle collisions in a Tonks gas are elastic, the system becomes integrable (it has "regular motion"), and the atoms cannot obtain a thermal equilibrium since the energy cannot divide itself equally between the particles. This system acts like a quantum Newton's cradle (this Newton's cradle gif animation is taken from Wikipedia).

The moral of this post is that there is a lot to consider when modelling a 1D Bose gas.

Saturday, 18 April 2009

High energy physics, e.g., at CERN, promises to discover physics beyond the standard model. However, it is not necessary to expend all this energy and money to probe fundamental physics. One can do so in tabletop experiments on cold atoms, molecules and ions.

Severalblog posts have recorded the recent appearance on the arxiv of a review by Ted Haensch of measurements of the fine structure constant by spectroscopy of cold atoms, ions and molecules. The idea is to compare very precise measurements at different times to detect any time dependence of the fine stucture constant, which would show physics beyond the standard model.

This current interest has reminded me of work by Ed Hinds to measure the electron electric dipole moment by observing the change in the energy levels of cold molecules on the application of a magnetic field. A non-zero value of such a quantity would show physics beyond the standard model. The Imperial College website has several pages of lucid explanation for the layperson here. Here is a chart from their website showing how precise they are trying to get.

Thursday, 9 April 2009

The title of this post is courtesy of a Simpsons episode where, to Homer's disappointment, the TV show "When dinosaurs get drunk" is replaced by "The boring world of Niels Bohr". Bohr's world, however, was anything but boring. He fled the Nazis from Denmark in a fishing boat during the rescue of the Danish Jews, and later worked on the Manhattan project to develop the first nuclear bomb. In earlier days, Bohr played football for a top Danish side (his brother played for the Denmark national team).

All this is to precede an addendum to my previous post about Bohr atoms: I neglected to consider interactions of Rydberg atoms with low frequency black-body radiation, which should cause stimulated transitions to nearby Rydberg states, thus decohering the quantum state; this could possibly be the principle cause of the classical type radiation.

Saturday, 4 April 2009

A colleague recently directed me to this paper (arxiv here), about entanglement and its philosophical consequences, by John Conway, of whom I was previously aware as a pure mathematician, and Simon Kochen.

The paper considers a system of two entangled spin-1 particles in separate locations, such that the total spin of the particles is zero. The authors assume that the observer (A) of one particle has free will to chose a set of axes in which to measure the squared components of the spin of the particle (i.e., he can make a choice of which axes to chose independent of his past history), and an observer of the other particle (B) has free will to measure the spin of this particle in one direction.

Furthermore, they assume the observers to be in motion such that A makes his measurement before B in A's inertial frame, but after B in B's inertial frame (temporal order is not invariant in relativity). The authors conclude that if we assume that the choices of A and B are free, then, in the same sense, the particles make a free choice (they give measurements independent of their past histories).

Saturday, 21 March 2009

Inspired by this post on the Uncertain Principles blog, and a talk I attended by Barry Dunning, I have recently become interested in Rydberg Bohr atoms. When quantum theory was in its infancy, Bohr proposed that electrons orbit atomic nucleii in certain classical orbits, much as planets orbit the Sun in our solar system. However, the biggest problem for this theory was that classical physics requires that charged particles, such as electrons, radiate light as they accelerate, and consequently lose energy. Such electrons would therefore be expected to spiral into the atomic nucleus whilst continuously emitting radiation.

Modern quantum mechanics tells us that electrons are not localised in space, but behave rather as waves, and their classical properties such as positions, momenta, energies and angular momenta may be only fuzzily defined (i.e., we can only know probabilistically the outcomes of their measurements). The electrons only radiate light when they are stimulated to by interacting with passing light (stimulated emission), or by interacting with the vacuum (spontaneous emission).

We expect quantum physics to reduce to classical physics in some limit; the nature of this limit is not well established - it could be the limit of large objects or many interactions with the environment. Rydberg atoms are atoms with an electron excited to a high energy state, such that the electron is likely to be found far away from the nucleus of the atom. In thesetwo recent papers, atoms are excited to a superposition of such Rydberg states so that their outer electrons are fairly localised in space, and orbit the atomic nucleii, much in the way of the Bohr atom. This is a classical limit, in the sense that the electron follows a classical trajectory, however, spontaneous emission of light from such atoms is fairly well suppressed (since the rate of emission scales in inverse proportion of the energy cubed). It actually seems that the lifetimes of the orbits are limited by the dephasing of the wavepacket (i.e., the orbit's quantum nature becomes important), rather than by spontaneous emission.

Nevertheless, it would be interesting to look at the spontaneous emission as a function of the expected angular momentum or position, and compare it to the classical radiation from an orbiting charge. Actually, I think I may attempt these calculations myself. I would normally be loath to describe my research ideas in a public forum incase I get scooped; however, I suspect that no-one reads this blog anyway.